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ATLANTA — Delta Air Lines Inc. has warned its pilots union that the struggling carrier’s cash reserves have fallen to the point where the company could seek to revise the agreement the two sides reached last year to avoid a bankruptcy filing at that time.

As part of the agreement for $1 billion in annual pilot concessions, Atlanta-based Delta included a bankruptcy protection letter that said the nation’s third-largest carrier would not seek more concessions unless its cash level fell below a certain point.

In a memo to pilots late Friday, the union said Delta has informed it that the company’s cash level has fallen below that point. The exact threshold was not specified in the memo, and the union and company declined to say what it is.

The company had $1.7 billion in unrestricted cash at the end of the second quarter. Analysts consider $1.5 billion as roughly the cash level at which an airline is in danger of bankruptcy.

While the company could ask for more cuts, it’s unlikely Delta would pursue any further concessions or significant changes to the pilot contract outside of bankruptcy because of how long such negotiations could take.

“The liquidity shortfall notice does not mean the company has decided to pursue any particular course of action at this time,” Delta spokesman John Kennedy said. “The company has not made any proposals to (the pilots union) at this time.”

Capt. John Malone, chairman of the pilot union’s executive committee, sought to reassure pilots in his memo Friday that negotiations for more cuts are not necessarily in the offing.

“The company also informed me that any such consultations will be in the context of a comprehensive business plan that is equitable and involves all other Delta stakeholders,” Malone said.

Despite the concessions it received last year from pilots, Delta’s financial situation has worsened amid persistently high fuel costs. The company has lost nearly $10 billion since January 2001 and has warned that while it is trying hard to avoid a Chapter 11 filing, it may not be able to.